Jimmy Bullard fires home the second of his two goals from the penalty spot during Hull City's 3-3 home draw with West Ham. Photograph: Hamish Blair/Getty Images

The two matches Hull City have played since Adam Pearson returned as chairman and publicly warned the manager Phil Brown that he would be judged on a week-by-week basis have seen the Tigers produce by far their most spirited performances of the season.

Many will point to another return, that of Jimmy Bullard, as the catalyst to a revival which suggests City have it in them to stay up after all. To be sure, the former Fulham midfielder was genuinely outstanding, his instinct for being available in space infallible, his distribution all but faultless. That his efforts should give him a hand in two goals was entirely appropriate for all that both – a deflected free-kick and a penalty even Brown admitted was soft – were fortunate.

But it is also the case that Brown has abandoned the negativity that made City's early season so depressing, playing two up front and having a go in the manner which saw them pick up so many points at the start of last season.

The fans have responded, giving the stadium the sort of atmosphere which cannot help but inspire a home team, and driven on by Bullard, City reacted so determinedly to going two down in the first 10 minutes that they went off at half-time in the lead.

Jimmy Bullard makes an impact for Hull that Dean Marney has been unable to emulate

The game changed soon after the interval, when Bernard Mendy was sent off for bringing down Scott Parker – almost as outstanding for the Hammers as Bullard was for Hull – and the visitors went on to rescue a point, but overall, it was a match which, despite both clubs' desperate financial straits, left you thinking both Brown and his opposite number Gianfranco Zola still have plenty of reasons for optimism.

Brown, whose own demeanour seems to have changed since Pearson's return, was asked what he thought about being judged on a weekly basis. "I accept it," he said, quietly. "I've been here before with Adam. When I first got the job from Phil Parkinson, the caretaker manager's role lasted for one game, then three games, then six games. It's a building-block process. We'll renew that old acquaintance and that working relationship."

Having just been told that his old friend and mentor Sam Allardyce would be having precautionary heart surgery, managerial pressure was very much on his mind. "We were talking about it coming back from the League Managers' Association dinner on Tuesday – it's not new, you're always under pressure to get results.

"But one of our supporters in Norway wrote to me requesting some semblance of sanity from the supporters – apparently we are, on aggregate, in 56th position out of 92 league clubs on our history. That doesn't put us in the Championship, it puts us in League One. It brought a little bit of reality to me."

Having described the game as both crazy and strange, Zola is confident West Ham would pull themselves out of trouble. "It's not the first time we have handled a game badly when we have been in control, and it's one of the things we will be talking about, but what I see is a team playing well, not very far from picking up victories instead of draws and defeats. We just need to improve certain things and we're going to be all right."